1math::bignum(n) Tcl Math Library math::bignum(n)
2______________________________________________________________________________
6
8 math::bignum - Arbitrary precision integer numbers
9
11 package require Tcl ?8.4?
12 package require math::bignum ?3.1?
14 ::math::bignum::fromstr string ?radix?
16 ::math::bignum::tostr bignum ?radix?
18 ::math::bignum::sign bignum
20 ::math::bignum::abs bignum
22 ::math::bignum::cmp a b
24 ::math::bignum::iszero bignum
26 ::math::bignum::lt a b
28 ::math::bignum::le a b
30 ::math::bignum::gt a b
32 ::math::bignum::ge a b
34 ::math::bignum::eq a b
36 ::math::bignum::ne a b
38 ::math::bignum::isodd bignum
40 ::math::bignum::iseven bignum
42 ::math::bignum::add a b
44 ::math::bignum::sub a b
46 ::math::bignum::mul a b
48 ::math::bignum::divqr a b
50 ::math::bignum::div a b
52 ::math::bignum::rem a b
54 ::math::bignum::mod n m
56 ::math::bignum::pow base exp
58 ::math::bignum::powm base exp m
60 ::math::bignum::sqrt bignum
62 ::math::bignum::rand bits
64 ::math::bignum::lshift bignum bits
66 ::math::bignum::rshift bignum bits
68 ::math::bignum::bitand a b
70 ::math::bignum::bitor a b
72 ::math::bignum::bitxor a b
74 ::math::bignum::setbit bignumVar bit
76 ::math::bignum::clearbit bignumVar bit
78 ::math::bignum::testbit bignum bit
80 ::math::bignum::bits bignum
82_________________________________________________________________
84
86 The bignum package provides arbitrary precision integer math (also
87 known as "big numbers") capabilities to the Tcl language. Big numbers
88 are internally represented at Tcl lists: this package provides a set of
89 procedures operating against the internal representation in order to:
90 · perform math operations
92 · convert bignums from the internal representation to a string in
94 the desired radix and vice versa. But the two constants "0" and
95 "1" are automatically converted to the internal representation,
96 in order to easily compare a number to zero, or increment a big
97 number.
98 The bignum interface is opaque, so operations on bignums that are not
100 returned by procedures in this package (but created by hand) may lead
101 to unspecified behaviours. It's safe to treat bignums as pure values,
102 so there is no need to free a bignum, or to duplicate it via a special
103 operation.
104
106 This section shows some simple example. This library being just a way
107 to perform math operations, examples may be the simplest way to learn
108 how to work with it. Consult the API section of this man page for
109 information about individual procedures.
110 package require math::bignum
112 # Multiplication of two bignums
114 set a [::math::bignum::fromstr 88888881111111]
115 set b [::math::bignum::fromstr 22222220000000]
116 set c [::math::bignum::mul $a $b]
117 puts [::math::bignum::tostr $c] ; # => will output 1975308271604953086420000000
118 set c [::math::bignum::sqrt $c]
119 puts [::math::bignum::tostr $c] ; # => will output 44444440277777
120 # From/To string conversion in different radix
122 set a [::math::bignum::fromstr 1100010101010111001001111010111 2]
123 puts [::math::bignum::tostr $a 16] ; # => will output 62ab93d7
124 # Factorial example
126 proc fact n {
127 # fromstr is not needed for 0 and 1
128 set z 1
129 for {set i 2} {$i <= $n} {incr i} {
130 set z [::math::bignum::mul $z [::math::bignum::fromstr $i]]
131 }
132 return $z
133 }
134 puts [::math::bignum::tostr [fact 100]]
136
139 ::math::bignum::fromstr string ?radix?
140 Convert string into a bignum. If radix is omitted or zero, the
141 string is interpreted in hex if prefixed with 0x, in octal if
142 prefixed with ox, in binary if it's pefixed with bx, as a number
143 in radix 10 otherwise. If instead the radix argument is speci‐
144 fied in the range 2-36, the string is interpreted in the given
145 radix. Please note that this conversion is not needed for two
146 constants : 0 and 1. (see the example)
147 ::math::bignum::tostr bignum ?radix?
149 Convert bignum into a string representing the number in the
150 specified radix. If radix is omitted, the default is 10.
151 ::math::bignum::sign bignum
153 Return the sign of the bignum. The procedure returns 0 if the
154 number is positive, 1 if it's negative.
155 ::math::bignum::abs bignum
157 Return the absolute value of the bignum.
158 ::math::bignum::cmp a b
160 Compare the two bignums a and b, returning 0 if a == b, 1 if a >
161 b, and -1 if a < b.
162 ::math::bignum::iszero bignum
164 Return true if bignum value is zero, otherwise false is
165 returned.
166 ::math::bignum::lt a b
168 Return true if a < b, otherwise false is returned.
169 ::math::bignum::le a b
171 Return true if a <= b, otherwise false is returned.
172 ::math::bignum::gt a b
174 Return true if a > b, otherwise false is returned.
175 ::math::bignum::ge a b
177 Return true if a >= b, otherwise false is returned.
178 ::math::bignum::eq a b
180 Return true if a == b, otherwise false is returned.
181 ::math::bignum::ne a b
183 Return true if a != b, otherwise false is returned.
184 ::math::bignum::isodd bignum
186 Return true if bignum is odd.
187 ::math::bignum::iseven bignum
189 Return true if bignum is even.
190 ::math::bignum::add a b
192 Return the sum of the two bignums a and b.
193 ::math::bignum::sub a b
195 Return the difference of the two bignums a and b.
196 ::math::bignum::mul a b
198 Return the product of the two bignums a and b. The implementa‐
199 tion uses Karatsuba multiplication if both the numbers are big‐
200 ger than a given threshold, otherwise the direct algorith is
201 used.
202 ::math::bignum::divqr a b
204 Return a two-elements list containing as first element the quo‐
205 tient of the division between the two bignums a and b, and the
206 remainder of the division as second element.
207 ::math::bignum::div a b
209 Return the quotient of the division between the two bignums a
210 and b.
211 ::math::bignum::rem a b
213 Return the remainder of the division between the two bignums a
214 and b.
215 ::math::bignum::mod n m
217 Return n modulo m. This operation is called modular reduction.
218 ::math::bignum::pow base exp
220 Return base raised to the exponent exp.
221 ::math::bignum::powm base exp m
223 Return base raised to the exponent exp, modulo m. This function
224 is often used in the field of cryptography.
225 ::math::bignum::sqrt bignum
227 Return the integer part of the square root of bignum
228 ::math::bignum::rand bits
230 Return a random number of at most bits bits. The returned num‐
231 ber is internally generated using Tcl's expr rand() function and
232 is not suitable where an unguessable and cryptographically
233 secure random number is needed.
234 ::math::bignum::lshift bignum bits
236 Return the result of left shifting bignum's binary representa‐
237 tion of bits positions on the left. This is equivalent to mul‐
238 tiplying by 2^bits but much faster.
239 ::math::bignum::rshift bignum bits
241 Return the result of right shifting bignum's binary representa‐
242 tion of bits positions on the right. This is equivalent to
243 dividing by 2^bits but much faster.
244 ::math::bignum::bitand a b
246 Return the result of doing a bitwise AND operation on a and b.
247 The operation is restricted to positive numbers, including zero.
248 When negative numbers are provided as arguments the result is
249 undefined.
250 ::math::bignum::bitor a b
252 Return the result of doing a bitwise OR operation on a and b.
253 The operation is restricted to positive numbers, including zero.
254 When negative numbers are provided as arguments the result is
255 undefined.
256 ::math::bignum::bitxor a b
258 Return the result of doing a bitwise XOR operation on a and b.
259 The operation is restricted to positive numbers, including zero.
260 When negative numbers are provided as arguments the result is
261 undefined.
262 ::math::bignum::setbit bignumVar bit
264 Set the bit at bit position to 1 in the bignum stored in the
265 variable bignumVar. Bit 0 is the least significant.
266 ::math::bignum::clearbit bignumVar bit
268 Set the bit at bit position to 0 in the bignum stored in the
269 variable bignumVar. Bit 0 is the least significant.
270 ::math::bignum::testbit bignum bit
272 Return true if the bit at the bit position of bignum is on, oth‐
273 erwise false is returned. If bit is out of range, it is consid‐
274 ered as set to zero.
275 ::math::bignum::bits bignum
277 Return the number of bits needed to represent bignum in radix 2.
278
280 bignums, math, multiprecision, tcl
281
283 Copyright (c) 2004 Salvatore Sanfilippo <antirez at invece dot org>
284 Copyright (c) 2004 Arjen Markus <arjenmarkus at users dot sourceforge dot net>
285math 3.1 math::bignum(n)